Volume of Combination of Solids

We saw how when calculating surface areas sometimes we add and sometimes we remove some areas as some surface area disappeared in the process of joining the seperate shapes. Lets see how we can calculate volumes of combination of solids.

Let's say you have the below treasure chest with you. You need to find our how much volume is holds so that you can fill up your treasure accordingly.

In the previous section, we have discussed how to find the surface area of solids made up of a combination of two basic solids. Here, we shall see how to calculate their volumes.

It may be noted that in calculating the surface area, we have not added the surface areas of the two constituents, because some part of the surface area disappeared in the process of joining them. However, this will not be the case when we calculate the volume.

The volume of the solid formed by joining two basic solids will actually be the sum of the volumes of the constituents, as we see in the examples below.

Following the same approach as earlier, how can we break up this image so that we get some basic shapes.

By separating the different sections, we have the two basic shapes, cuboidspherecone and cylinderspherecone.

But observe closely that we actually dont have a full cylinder. We have just halfquarter a cylinder.

So the volume of our treasure chest is volume of the cuboid + 12 volume of the cylinder.

Now, if the length, breadth and height of the cuboid are 15 m, 7 m and 8 m, respectively and if the diameter of the half cylinder is 7 m and its height is 15 m, the volume of the treasure chest is m3 (Upto two decimal places).